 ### fix more math

parent 437023a7
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 ... ... @@ -489,12 +489,12 @@ the eigenfunctions of $L$. Recall that q quantum state $|\phi\rangle$ can be written in an orthonormal basis $\{ |u_n\rangle \}$ as $$\|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$ $$|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$ In terms of hermitian operators and their eigenfunctions, the eigenfunctions play the role of the orthonormal basis. In reference to our running example, the 1D Schrödinger equation of a free particle, the eigenfunctions $\sin(\frac{n \pi x}{L})$ play the role of the basis functions $\ket{u_n}$. $\sin(\frac{n \pi x}{L})$ play the role of the basis functions $|u_n\rangle$. To close our running example, consider the initial condition $\psi(x,o) = \psi_{0}(x)$. Since the eigenfunctions $\sin(\frac{n \pi x}{L})$ ... ... @@ -583,7 +583,7 @@ necessary to work with numerical methods of solution. 6. [:sweat:] We consider the Hilbert space of functions $f(x)$ defined for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$. Which of the following operators on this space is hermitian? Which of the following operators on this space is Hermitian? (a) $L = A(x) \frac{d^2 f}{dx^2}$ ... ...
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